We examine the design of the modulation classifiers, which identify the modulation type of received noisy signals in this research. The family of modulation schemes of our concern is the quadrature amplitude modulation, which has been widely used in modern digital communication. Modulation recognition has been traditionally viewed as a hypothesis test problem with a fixed sample size. Because the amount of received data increases with time, we formulate the problem as a variable sample size test, and propose an iterative recognition procedure. The new approach called the sequential probability ratio test has important advantages, including low error rate, low computational complexity and flexible tradeoff between performance and speed.